# Numerically Stable Evaluation of Moments of Random Gram Matrices with Applications

## TL;DR

This paper introduces a numerically stable method for computing positive moments of one-side correlated random Gram matrices, improving accuracy in high-dimensional settings and enabling better eigenvalue distribution approximations.

## Contribution

It provides a new stable closed-form approach for evaluating moments of correlated Gram matrices, enhancing numerical accuracy over existing methods.

## Key findings

- The method achieves higher numerical stability in high-dimensional regimes.
- It allows accurate approximation of eigenvalue distributions.
- The approach improves the reliability of moment-based spectral analysis.

## Abstract

This paper is focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed-form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment based-approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.